A computational model is developed to analyze the geometrically nonlinear response of porous functionally graded shells when subjected to various mechanical loadings and boundary conditions. This mathematical modeling is based on High-Order-Shear Deformation Theory (HSDT) using double directors vectors. The material properties are supposed to vary continuously along the thickness referring to power law distribution including even and uneven porosity distributions. The nonlinear shell model is developed using a weak form formulation. Then, a finite element model based on an isoparametric concept is employed. A convergence analysis is carried out to determine the minimum required number of elements in the numerical simulations. The potential of the presented nonlinear shell modeling is highlighted through comparisons between linear and nonlinear formulations with their counterparts in the literature. Very good agreements are obtained between the numerical simulations of the developed model with previous results of various kinds of plates subjected to different loadings and porosity distributions. The nonlinear shell modeling, material gradation, and porosity effects are also examined for complex structures including bioinspired ring and cylindrical panel. It is shown that the porosity and material gradation have significant effects on the ring's displacement and shear stress. As for the cylindrical roof-like panel, it is demonstrated that the linear formulation gives erroneous results for the displacement without detecting the snap-through phenomenon due to the large deformation of the structure. The results show the significant effect of the porosity distribution type of the response of complex dynamical systems.

The objective of the present paper is to predict numerically the effect of low velocity impact on the composite epoxy reinforced with quasi-unidirectional flax fabrics. The composite circular plate is meshed with a solid shell finite element (SS). Only one element in the thickness direction is adopted. This SS element is implemented into the user element (UEL) interface of ABAQUS in order to overcome numerical locking problems that may occurred when using the ABAQUS solid and shell elements. The epoxy/flax composite is characterized by a elasto-visco-plastic behavior. The Hill’s anisotropic criterion of plasticity with isotropic hardening and the Johnson-Cook viscoplastic model are applied. The simulations are accomplished via ABAQUS/Standard. The obtained results present the efficiency of the developed model using one solid shell element in the thickness direction from a computational point of view.

The main objective of this work is to develop an hexahedral solid shell finite element in order to resolve the numerical locking effects that may have occurred when employing the conventional solid and shell finite elements. The developed formulation relay on the coupling between the Assumed Natural Strain (ANS) and Enhanced Assumed Strain (EAS) methods. The FE model was implemented into the user element (UEL) interface of the FE commercial code ABAQUS by using the UEL FORTRAN subroutine. The robustness and performance of this element are proven using dynamic contact metal sheet behavior at low velocity impact. The obtained results are validated with finding from the literature. The developed solid shell element is efficient from a computational view point as the thickness direction is discretized adopting only single element layer.

This study is focusing on the finite element simulation of low velocity impact applied to glass fiber-reinforced composites. Elasto-visco-plasticity is adopted taking into account strain rate effect, with isotropic hardening. To avoid numerical locking, hexahedral solid shell finite element SS is developed. The formulation is based on the mixed Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) methods. A geometrical non linear condition is applied. The finite element is implemented in UEL subroutine via the commercial software ABAQUS/Standard. The numerical element proved its efficiency comparing to conventional element and previous experimental results in (Mars et al. 2018). Numerical simulations with solid element are conducted using Abaqus/standard via user material UMAT subroutine. In terms of computation time, the solid shell element is less time consuming when comparing to conventional solid element. This is due to the fact that a single element through the thickness direction is adopted. Element efficiency is assessed for various fibers contents.

The main objective of this paper is to develop a numerical model susceptible to solve the numerical locking problems that may appear when applying the conventional solid and shell finite elements of ABAQUS. This model is based on a hexahedral solid shell element. The formulation of this element relays on the combination of the enhanced assumed strain (EAS) and assumed natural strain (ANS) methods with modified First Shear Deformation Theory (FSDT). The developed element is implemented into the ABAQUS user element (UEL) interface. The performance of this element is demonstrated by different benchmark tests from the literature. Our contribution consists on applying a single solid shell element through the thickness direction to predict the low velocity impact behavior on functionally graded material (FGM) circular plates.

In this paper, the formulation of the finite element method for vibro-acoustic problem is applied to a vehicle to investigate the sound pressure level inside the cabin. This study is combined with a stochastic analysis to account for variability of different parameters, considered as random variables, which are related to the characteristics of materials and boundary conditions. The results show that the Generalized Polynomial Chaos (gPC) method is more efficient compared to the direct Monte Carlo simulation (MC) without causing significant loss of accuracy. It is also shown that uncertainty levels in the input data could result in large variability in the calculated interior sound pressure level. The result of this modeling strongly depends on the order of the Polynomial Chaos. An increase in this order is accompanied by a better projection of the solution.

This paper presents an implementation of a fully coupled non-associated anisotropic plasticity-ductile damage model, including a mixed nonlinear isotropic- kinematic hardening. With the non-associated anisotropic plasticity assumption, the yielding and plastic potential are determined independently. The quadratic Hill’48 function is considered for yield and plastic potential to describe the anisotropic plastic behavior of DD13 sheets. A three non-linear local scalar equation problem is solved using the Newton–Raphson method. The numerical resolution of the proposed algorithm is implemented into ABAQUS using the user interface material subroutines (UMAT and VUMAT). A consistent tangent operator is developed to preserve the quadratic rate of asymptotic convergence that characterizes Newton's method. The evaluation of the proposed implementation ability to predict the real behavior of DD13 steel material during forming is achieved using some experimental setups performed by the authors.

In this paper, an improved anisotropic elasto-plastic model strongly coupled with isotropic ductile damage is investigated. The quadratic Hill'48 yield criterion and non-linear isotropic/kinematic hardening are considered in the associated flow rule model. The numerical formulation of the proposed model is implemented in ABAQUS finite element code via the user material subroutines UMAT and VUMAT. The mechanical behavior of DD13 sheet metal is investigated. Its significant deep drawing capability makes this material attractive, particularly for the automotive industry. An experimental database of the DD13 mechanical properties is achieved through a serie of uniaxial tensile tests, so that the anisotropic coefficients, hardening and damage parameters are obtained. For validation purpose, the numerical results are compared to Erichsen cupping test. The combined experimental/numerical study proves the ability of the proposed model in the description of the DD13 damaged-anisotropic behavior with good accuracy.

This paper deals with the implementation of an anisotropic plasticity constitutive equations exhibiting non-linear isotropic, kinematic hardening and coupled continuum ductile damage models. A fully implicit integration of the coupling constitutive equations is adopted and leads to two non-linear local scalar equations solved using the Newton method. The consistent local tangent modulus is obtained in a closed form by exact linearization of the algorithm. The numerical treatment of the proposed algorithm is implemented on ABAQUS using user interface material subroutines (UMAT and VUMAT). The performance of the present algorithm is assessed and bared out by numerical examples.

Flexible forming with rubber pad is a forming technique that is commonly used in the aeronautic and automotive industries to produce parts with complex shapes from thin sheet metal. The purpose of this chapter is to compare between using flexible punch or flexible die in sheet metal forming with rubber pad. A finite element simulation is carried out to predict the behavior of the flexible stamping process of aluminum sheet metal with the two techniques of forming. For the sheet metal, an elastoplastic constitutive model is adopted and implemented in ABAQUS/Standard software via UMAT subroutine. However, a Mooney–Rivlin hyperelastic model is adopted for the rubber pad. Results predicted numerically consist of comparing the variation of some key parameters process using two deformation styles in order to produce safety parts without localized severe deformation. It was found that using rubber as flexible die may reduce the thinning rate and values of equivalent plastic strain in the formed part. Also, based on the Forming Limit Diagram (FLD) analysis, using flexible die instead of flexible punch may successfully form part without necking and micro crack and without localized severe deformation that can lead to fracture.

In this work, an analytical formulation and numerical implementation of the response of the coupled structure acoustic system were performed. The acoustic pressure inside the cavity as well as the plate displacement are analyzed. This study is combined with a probabilistic analysis to account for variability of different parameters, considered as random variables, which are material properties. A reliability based design optimization (RBDO) using the generalized polynomial chaos (gPC) is addressed. In order to reduce the computational cost of the classical approach of RBDO problem, the optimum safety factor (OSF) method coupled with the gPC procedure is applied to the coupled acoustic-structure systems. Numerical examples showed the effectiveness and efficiency of the OSF based on gPC for the reliability optimization of the structural-acoustic system with probabilistic random variables. (C) 2017 Elsevier Ltd. All rights reserved.

The purpose of this paper is to study numerically the “elastomer-assisted compression beading” (EACB process). It consists of conventional compressing beading after a local bulging carried out by an elastomer material. A Finite Element Method (FEM) is introduced to predict where and when the damage can occur in the tube and to study the effects of anisotropy on the occurrence of failure by cracking in regions where damage is accumulated. An anisotropic elasto-plastic constitutive model with mixed non-linear isotropic/kinematic hardening fully coupled with Lemaitre's ductile damage is implemented in ABAQUS/Explicit software via VUMAT subroutine. The influence of anisotropy on the damage evolution is investigated in this study and results are compared with isotropic model.

In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is investigated using Abaqus software. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the FG shells in large displacements and rotations. The material properties are introduced according to the integration points in Abaqus via the UMAT subroutine. The predictions of static response of several non-trivial structure problems are compared to some reference solutions in order to verify the accuracy and the effectiveness of the new developed nonlinear solution procedures. All the results indicate very good performance in comparison with references.

A finite element implementation of an anisotropic plasticity model for aluminum AA5754-O in impact simulations was performed, particularly for the case of perforation on low velocity (up to about 25 m/s). The elasto-viscoplastic model includes isotropic elasticity, anisotropic yielding, associated plastic flow and mixed non-linear isotropic/kinematic hardening. Coupling between elasto-viscoplastic model and isotropic ductile damage is investigated. Strain rate is integrated in numerical modeling. The material model is implemented into a user-defined material (VUMAT) subroutine for the commercial finite element code ABAQUS/Explicit to predict the numerical response of circular aluminum plate subjected to low velocity impact. Results include the effect of anisotropy on the material behavior. It is shown that anisotropy plays a significant role in penetration of the present plate material.

Rubber forming is a sheet metal forming process using flexible punch or die. In this paper, finite element method is introduced to analyze rubber-pad forming process of aluminum sheet metal. An elasto-plastic constitutive model with J2 yield criterion and mixed non-linear isotropic/kinematic hardening coupled with Lemaitre's ductile damage has been adopted during flexible forming operation. To model rubber material, a Mooney-Rivlin theory is used in the finite element simulation. A stamping of aluminum sheet metal with soft punch is simulated. A fully coupled elasto-plastic damage model is implemented in ABAQUS/Standard software via UMAT subroutine to study the effect of some key process parameters like hardness of rubber, type of rubber on the variation of the thickness, the springback and damage of aluminum sheet metal.

L’une des preoccupations majeures dans la production de profiles composites a matrice thermoplastique par le procede de pultrusion est de reussir l’impregnation de la resine thermoplastique par le reseau de fibres de renfort, tout en realisant une forme correcte et en conservant une excellente resistance aux chocs. En effet, l’impregnation est un processus difficile en raison de la viscosite elevee des thermoplastiques a l’etat fondu. Une etude analytique et experimentale de l’etat de l’impregnation a ete menee. Celle-ci permet de prevoir notamment la permeabilite et la pression capillaire mise en jeu lors de la progression capillaire. Les proprietes du renfort et la distribution des fibres sont mises en evidence notamment grâce a la microtomographie X. Ce travail a pour objectif industriel la fabrication de profiles pultrudes complexes pour application aeronautique.